jmc

Subtracting 3 from both sides of the equation, we have $x^2-4x+4=16$, which indicates that the fastest way to solve this problem would be to complete the square. Thus, we have $(x-2{)}^2=16$, or $x-2=\pm 4$, or $x=6$ and $x=-2$. Since $a\ge b$, we now know that $a=6$ and $b=-2$, so $2a+b=2(6)-2=\boxed{10}$.